Regression by dependence minimization and its application to causal inference in additive noise models

By Joris M. Mooij, Dominik Janzing, Jan Peters, Bernhard Schölkopf. 2009

168 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability, Causal Inference & Discovery

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Citations in the corpus

Counterfactual Fairness (2017, background): “[26]), but this concernsM and not Ŷ , and is motivated by explicit assumptions about structural equations, as described next.”
Toward Causal Representation Learning (2021, background): “, with the roles of X and Y interchanged) [18], [113], [139], [175], [190] (see also [246]).”
Towards Causal Representation Learning (2021, background): “[237, 188, 229, 113, 174, 187, 139, 17, 246, 277, 175, 123, 186, 176, 36, 82, 161], learning causal relations frequently requires collecting data from multiple environments, or the ability to perform interventions [251].”
Learning explanations that are hard to vary (2020, background): “…2012].14 Based on this insight, it was proposed that regression based on causal features should presents desirable invariance and robustness properties [Mooij et al., 2009, Schölkopf et al., 2012, Peters et al., 2016, Rojas-Carulla et al., 2018, Heinze-Deml et al., 2018, von Kügelgen et al., 2018].”
Invariant Causal Prediction for Sequential Data (2017, background): “(The nature of this idea is similar to the one proposed in Mooij et al. (2009), in which the authors evaluate the goodness of a regression function by the independence between residuals and predictors rather than the residual variance.”
On causal and anticausal learning (2012, methodology): “We modify the algorithm of Mooij et al. (2009) to obtain the shared function φ, enforcing separate independence C ⊥ NE and C ′ ⊥ N ′E .”
Identifiability of Causal Graphs using Functional Models (2011, methodology): “…case described above, practical methods for causal inference using ANMs have been suggested for the multivariate case [Hoyer et al., 2009, Zhang and Hyvärinen, 2009, Mooij et al., 2009, Tillman et al., 2009]: whenever a graph models the data the method infer this structure as the causal graph.”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, methodology): “…been proposed in recent years (Friedman and Nachman, 2000; Kano and Shimizu, 2003; Shimizu et al., 2006; Sun et al., 2006, 2008; Hoyer et al., 2009; Mooij et al., 2009; Zhang and Hyvärinen, 2009; Janzing et al., 2010; Mooij et al., 2010; Daniušis et al., 2010; Mooij et al., 2011; Shimizu et al.,…”
CAM: Causal Additive Models, high-dimensional order search and penalized regression (2013, methodology): “Identiﬁability results for this model class has been given by Mooij et al. (2009) and Peters et al. (2013).”
Causal Inference on Discrete Data Using Additive Noise Models (2009, methodology): “[11] and the practical approach of combining constraint-based methods and ANMs by Tillman et al.”
Identiﬁability of Causal Graphs using Functional Models (methodology): “The algorithm is based on [Mooij et al., 2009] but outputs all graphs that are consistent with the data by using depth-ﬁrst search: whenever there is more than one way to proceed in building the DAG, instead of choosing the one that leads to the highest p -value of the independence test (see…”
Robust Learning via Cause-Effect Models (2011, methodology): “We apply the algorithm of [12] to obtain the shared function φ , enforcing separate independence C ⊥⊥ N E and C (cid:48) ⊥⊥ N E .”
Justifying Additive Noise Model-Based Causal Discovery via Algorithmic Information Theory (2009, methodology): “Here we focus on a method [6, 14, 13] that yielded quite encouraging results on real data sets and show that it also can be justified via algorithmic information theory.”
UvA-DARE ( Digital Academic Repository ) Causal Discovery with Continuous Additive Noise Models (2014, unknown): “Algorithm 1 is a slightly modiﬁed version of the one proposed in Mooij et al. (2009).”
Causal Inference via Kernel Deviance Measures (2018, methodology): “Another group of methods [9, 25, 14] postulates that there is some inherent asymmetry between cause and effect and proposes different asymmetry measures that form the basis for causal discovery.”